Recently, to reduce a driver's burden in driving a vehicle, a technique of controlling a running state of a vehicle on the basis of a running state of a preceding vehicle has attracted attention. A driving support system described in Patent Literature 1 is known as such a follow-up run control technique. In such a system, inter-vehicle control is carried out by considering a preceding vehicle of a vehicle and a pre-preceding vehicle as a temporary preceding vehicle and selecting one larger in target deceleration or one smaller in target acceleration out of the preceding vehicle and the pre-preceding vehicle as a tracking target.